title: Self-oscillatory dynamics of the metabolic process in a cell.
abstract: In this work, a mathematical model of self-oscillatory dynamics of the metabolism in a cell is studied. The full phase-parametric characteristics of variations of the form of attractors depending on the dissipation of a kinetic membrane potential are calculated. The bifurcations and the scenarios of the transitions "order-chaos", "chaos-order" and "order-order" are found. We constructed the projections of the multidimensional phase portraits of attractors, Poincaré sections, and Poincaré maps. The process of self-organization of regular attractors through the formation torus was investigated. The total spectra of Lyapunov exponents and the divergences characterizing a structural stability of the determined attractors are calculated. The results obtained demonstrate the possibility of the application of classical tools of nonlinear dynamics to the study of the self-organization and the appearance of a chaos in the metabolic process in a cells.
authors.affiliation: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kyiv. vgrytsay@bitp.kiev.ua
authors.forename: V I
authors.initials: VI
authors.lastname: Grytsay
authors.forename: I V
authors.initials: IV
authors.lastname: Musatenko
mesh_terms: D001173:Arthrobacter / Q000378:metabolism*; D019149:Bioreactors / Q000382:microbiology; D003198:Computer Simulation; D007700:Kinetics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D009991:Oscillometry; D010507:Periodicity; D013256:Steroids / Q000378:metabolism*
chemical_list: D013256:Steroids